The paper deals with a distributed parameter system related to the so-called fixed-bed bioreactor. The original nonlinear partial differential system is linearized around the steady state. We find that the linearized system is not exactly controllable but it is approximatively controllable when certain algebraic equations hold. We apply frequency-domain methods (transfer function analysis) to consider a related output tracking problem. The input-output system can be formulated as a translation invariant pseudodifferential equation. A simulation shows that the calculation scheme is stable. An idea to use frequency-domain methods and certain pseudodifferential operators for parametrization of control systems of more general systems is pointed out.
"On controllability, parametrization, and output tracking of a linearized bioreactor model." J. Appl. Math. 2003 (5) 243 - 276, 30 April 2003. https://doi.org/10.1155/S1110757X03204046